Kuliah materi MEKANIKA MATERIAL BAHAN

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MEKANIKA MATERIAL (BAHAN)

1.

Jenis pembebanan pada material

2.

Jenis tegangan (stress)

3.

Perhitungan kekuatan material untuk

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Terminology for Mechanical Properties

_Stress_{- Force or load per unit area of cross-section over}

which the force or load is acting.

 _Strain_{- Elongation change in dimension per unit length.}  _{Young’s modulus}_{- The slope of the linear part of the}

stress-strain curve in the elastic region, same as modulus of elasticity.

 _{Shear modulus (G)}_{- The slope of the linear part of the}

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Tegangan Normal (): intensitas gaya yang bekerja tegak lurus bidang irisan

contoh: Tensile stress, ()

Area, A

Ft Ft

  Ft

A_o original area before loading Area, A Ft Ft Fs F F

Fs

 

F

s

A

o

Stress has units: N/m2 (or lb/in2 )

Engineering Stress

Tegangan geser (): intensitas gaya yang bekerja sejajar bidang irisan

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Gaya Hoop pada bejana tekan

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Pure Tension Pure Compression

Pure Shear

Pure Torsional Shear _e Fnormal

A_o

_e l  l o

l _o

_e Fshear

A_o

tan stress

strain

stress

strain



_e



G





_e



E



Elastic response

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MEKANIKA BAHAN KONSEP STRESS Gage length P P P P

Yield stress,  _y

Ultimate stress,  _u

Stress, 

Strain, 

1 2

3 4 5

1. Linear elastic: region of proportional elastic loading 2. Nonlinear elastic: up to yield

3. Perfect plasticity: plastic flow at constant load

4. Strain hardening: plastic flow with the increase of stress 5. Necking: localization of deformation and rupture

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 

Linear Elastic

Nonlinear Elastic

 

Unloading Loading

p Extension Contraction Shearing

 Hooke’s law for extension:

σ = E 

 Hooke’s law for shear:

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A

V





V

A



_in Psi Ksi

lb Psi MPa Pa m N Pa 1 10 1 1 1 1 10 1 1 1 3 2 6 2    

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F

p

F

F F

F F F F d t t t t

Cylindrical bolt or rivet

a

t









 Hooke’s law for extension:

σ = E 

 Hooke’s law for shear:

 = G 

)

1

(

2





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

1



h



u



h

u





h

u



tan(



)



1







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n

or

n

or

u

y

allow

u

y

allow





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•

Simple

tension: cable

o

 

F

A

•

Simple

shear: drive shaft

Ao = cross sectional Area (when unloaded)

F



o

 

Fs

A



Note:  = M/AcR here.

Ski lift (photo courtesy P.M. Anderson)

M

A

o

2R

Fs

A

c

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[image:35.720.52.642.40.433.2]

(c )2 00 3 B ro ok s/ C ol e, a d iv is io n of T ho m so n L ea rn in g, I nc . T ho m so n L ea rn in g™ is a tr ad em ar k us ed h er ei n un de r lic en se .

Figure. A unidirectional force is applied to a specimen in the tensile test by means of the moveable crosshead. The cross-head movement can be performed using screws or a hydraulic mechanism

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Properties Obtained from the Tensile

Test

 _{Elastic limit}

 _{Tensile strength, Necking}  _{Hooke’s law}

 _{Poisson’s ratio}

 Modulus of resilience (E_r)  _{Tensile toughness}

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[image:38.720.55.628.38.366.2]

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[image:39.720.43.680.91.419.2]

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cup-and-cone fracture in Al

[image:40.720.406.674.256.474.2]

brittle fracture in mild steel

Figure. Localized

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• Maximum possible engineering stress in tension.

• Metals: occurs when necking starts. • Ceramics: occurs when crack propagation

starts.

• Polymers: occurs when polymer backbones

are

aligned and about to break.

(Ultimate) Tensile Strength,

σ

_TS

_y

strain

Typical response of a metal

F = fracture or

ultimate strength

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Deformation

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cup-and-cone fracture in Al

[image:46.720.501.675.24.116.2]

brittle fracture in mild steel

Figure. Localized

deformation of a ductile material during a tensile test produces a necked region

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Rod AB

Rod BC

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